Question

Comparing square roots using estimated values, plot √0.5 on the number line. What is the approximate value of √0.5?

1) 0.3
2) 0.4
3) 0.6
4) 0.7

Answer 1

The approximate value of √0.5 is 0.7, which is closest to its actual value when compared to other choices. This value can be plotted on a number line closer to 1 than to 0.

Step-by-step explanation:

In mathematics, specifically dealing with square roots, we can estimate the value of √0.5 by comparing it to perfect squares. Knowing that √1 is 1 and √0 is 0, the value of √0.5 lies between 0 and 1. If we consider the squares of the answer choices given:

• 0.3² = 0.09
• 0.4² = 0.16
• 0.6² = 0.36
• 0.7² = 0.49

The value that is closest to 0.5 when squared is 0.7, as 0.7² = 0.49. Therefore, the approximate value of √0.5 is 0.7.

To plot √0.5 on a number line, we locate the point between 0 and 1 that is slightly less than the midpoint (which is 0.5). Since the estimated square root is 0.7, this point would be closer to 1 than to 0.